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Inverse Galois theory

Author: Gunter Malle; B Heinrich Matzat
Publisher: Berlin ; New York : Springer, ©1999.
Series: Springer monographs in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Gunter Malle; B Heinrich Matzat
ISBN: 3540628908 9783540628903
OCLC Number: 42002767
Description: xv, 436 pages : illustrations ; 25 cm.
Contents: Ch. I. The Rigidity Method --
1. The Inverse Galois Problem over C(t) and R(t) --
2. Arithmetic Fundamental Groups --
3. Fields of Definition of Galois Extensions --
4. The Rigidity Property --
5. Verification of Rigidity --
6. Geometric Automorphisms --
7. Rational Translates of Galois Extensions --
8. Automorphisms of the Galois Group --
9. Computation of Polynomials with Prescribed Group --
10. Specialization of Geometric Galois Extensions --
Ch. II. Applications of Rigidity --
1. The General Linear Groups --
2. Pseudo-Reflection Groups and Belyi Triples --
3. The Classical Groups --
4. The Exceptional Groups of Rank at Most 2 --
5. The Exceptional Groups of Large Rank --
6. Galois Realizations of Linear and Unitary Groups over Q --
7. Galois Realizations of Symplectic and Orthogonal Groups over Q --
8. Galois Realizations of Exceptional Groups over Q --
9. The Sporadic Groups --
10. Summary for Simple Groups --
Ch. III. Action of Braids --
1. Braid Groups --
2. Profinite Braid Groups --
3. Galois Descent --
4. Cyclic Polynomials --
5. Rigid Braid Orbits --
6. Unramified Rational Places --
7. Braids and Geometric Automorphisms --
8. Ramified Rational Places --
9. Outer Automorphism Groups as Galois Groups --
10. Finite Quotients of the Braid Group as Galois Groups --
Ch. IV. Embedding Problems --
1. Geometric Embedding Problems --
2. Split Embedding Problems with Abelian Kernel --
3. Embedding Problems with Centerless Kernel --
4. Verification of the GAR-Property --
5. Frattini Embedding Problems --
6. The Quadratic Trace Form --
7. Brauer Embedding Problems --
8. Concordant Embedding Problems --
9. The Hasse Embedding Obstruction --
10. Nilpotent Galois Groups over Global Fields --
Ch. V. Rigid Analytic Methods --
1. Results from Rigid Analytic Geometry --
2. The Inverse Problem over Q[subscript p](t) and F[subscript p](t) --
3. Free Quotients of the Fundamental Group --
4. Large Fields --
5. On the Fundamental Group with Restricted Ramification.
Series Title: Springer monographs in mathematics.
Responsibility: Gunter Malle, B. Heinrich Matzat.
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